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Research Article | Open Access

Convergence rates of the modified forward reflected backward splitting algorithm in Banach spaces

Weibo Guan, Wen Song( )
School of Mathematical Sciences, Harbin Normal University, Harbin 150025, China
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Abstract

Consider the problem of minimizing the sum of two convex functions, one being smooth and the other non-smooth in Banach space. In this paper, we introduce a non-traditional forward-backward splitting method for solving such minimization problem. We establish different convergence estimates under different stepsize assumptions.

Keywords

convergence rateforward-backward splitting algorithmBanach spaces
CLC number: 65K05, 90C25, 90C30

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AIMS Mathematics
Volume 8 Issue 5,
May 2023
Pages 12195-12216
DOI: 10.3934/math.2023615

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Guan W, Song W. Convergence rates of the modified forward reflected backward splitting algorithm in Banach spaces. AIMS Mathematics, 2023, 8(5): 12195-12216. https://doi.org/10.3934/math.2023615

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Received: 28 January 2023
Revised: 12 March 2023
Accepted: 14 March 2023
Published: 15 May 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)